This article introduces funGp, an R package which handles regression problems involving multiple scalar and/or functional inputs, and a scalar output, through the Gaussian process model. This is particularly of interest for the design and analysis of computer experiments with expensive-to-evaluate numerical codes that take as inputs regularly sampled time series. Rather than imposing any particular parametric input-output relationship in advance (e.g., linear, polynomial), Gaussian process models extract this information directly from the data. The package offers built-in dimension reduction, which helps to simplify the representation of the functional inputs and obtain lighter models. It also implements an Ant Colony based optimization algorithm which supports the calibration of multiple structural characteristics of the model such as the state of each input (active or inactive) and the type of kernel function, while seeking for greater prediction power. The implemented methods are tested and applied to a real case in the domain of marine flooding. The funGp package is downloadable from GitHub (https://github.com/djbetancourt-gh/funGp) and CRAN (https://cran.r-project.org/package=funGp).